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King School has an enrollment of 900 students. The school day consists

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King School has an enrollment of 900 students. The school day consists  [#permalink]

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New post 21 Sep 2019, 03:17
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King School has an enrollment of 900 students. The school day consists of 6 class periods during which each class is taught by one teacher. There are 30 students per class. Each teacher teaches a class during 5 of the 6 class periods and has one class period free. No students have a free class period. How many teachers does the school have?

A. 25
B. 30
C. 36
D. 60
E. 150


PS15402.01
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Re: King School has an enrollment of 900 students. The school day consists  [#permalink]

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New post 21 Sep 2019, 04:01
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gmatt1476 wrote:
King School has an enrollment of 900 students. The school day consists of 6 class periods during which each class is taught by one teacher. There are 30 students per class. Each teacher teaches a class during 5 of the 6 class periods and has one class period free. No students have a free class period. How many teachers does the school have?

A. 25
B. 30
C. 36
D. 60
E. 150


PS15402.01


Each classroom has 30 students
—> Total number of classrooms = 900/30 = 30

Total number of classes happen in a day = 30*6 = 180

Let the total number of teachers = x
Since, each teacher takes 5 classes in a day, total number of classes that happen in a day = 5x

—> 5x = 180
—> x = 36

IMO Option C

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Re: King School has an enrollment of 900 students. The school day consists  [#permalink]

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New post 21 Sep 2019, 05:24
total classes 900/30 = 30
and each class has 6 periods so total periods in school ; 30*6
1 teacher takes at most 5 classes so total teachers in school ; 30*6/5 = 36
IMO C



gmatt1476 wrote:
King School has an enrollment of 900 students. The school day consists of 6 class periods during which each class is taught by one teacher. There are 30 students per class. Each teacher teaches a class during 5 of the 6 class periods and has one class period free. No students have a free class period. How many teachers does the school have?

A. 25
B. 30
C. 36
D. 60
E. 150


PS15402.01
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King School has an enrollment of 900 students. The school day consists  [#permalink]

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New post 21 Sep 2019, 06:29
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gmatt1476 wrote:
King School has an enrollment of 900 students. The school day consists of 6 class periods during which each class is taught by one teacher. There are 30 students per class. Each teacher teaches a class during 5 of the 6 class periods and has one class period free. No students have a free class period. How many teachers does the school have?

A. 25
B. 30
C. 36
D. 60
E. 150


PS15402.01


No student has a free period.
Thus, all 900 students are taught each period, implying that each period is composed of the same number of 30-student classes.
Every teacher teaches 5 of the 6 periods.
Thus, every teacher teaches exactly 5 classes.

We can PLUG IN THE ANSWERS, which represent the number of teachers.
When the correct answer is plugged in, the total number of students taught each period = 900.

B: 30
Since each of the 30 teachers teaches 5 classes, the total number of classes = 30*5 = 150.
Since these 150 classes are divided equally among 6 periods, the number of classes per period \(= \frac{150}{6} = 25\).
Since each of these 25 classes is composed of 30 students, the total number of students taught each period = 25*30 = 750.
Too small.

D: 60
Doubling the number of teachers from 30 to 60 will double the number of students taught each period from 750 to 1500.
Too big.

Since B yields a result that is TOO SMALL and D a result that is TOO BIG, the correct answer must be BETWEEN B AND D.


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Re: King School has an enrollment of 900 students. The school day consists  [#permalink]

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New post 11 Dec 2019, 21:40
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Hi All,

We're told that King School has an enrollment of 900 students. The school day consists of 6 class periods during which each class is taught by one teacher and there are 30 students per class. However, each teacher teaches a class during 5 of the 6 class periods and has one class period free (but NO students have a free class period). We're asked for the number of teachers that the school has. This question provides us with all of the 'numbers' that we need to answer the question, but you can still perform the necessary calculations in a number of different ways. As such, how you organize your information will impact how quickly you can answer the question.

To start, since each class consists of 30 students, we know that 900/30 = 30 classes run each period.

Since the School runs 6 class periods a day, we will need (6)(30) = 180 teacher-periods to be covered by the teachers.

Each teacher covers 5 teacher-periods a day though (NOT 6), so we need 180/5 =36 teachers to cover all of the classes.

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Re: King School has an enrollment of 900 students. The school day consists  [#permalink]

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New post 12 Dec 2019, 06:24
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gmatt1476 wrote:
King School has an enrollment of 900 students. The school day consists of 6 class periods during which each class is taught by one teacher. There are 30 students per class. Each teacher teaches a class during 5 of the 6 class periods and has one class period free. No students have a free class period. How many teachers does the school have?

A. 25
B. 30
C. 36
D. 60
E. 150


PS15402.01


There are 900 students, and there are 30 students per class.
900/30 = 30
So, at any given time during the school day, there are 30 class periods happening.

Since there are 6 class periods per day, the TOTAL number of classes each day = (6)(30) = 180

Each teacher teaches 5 classes per day
If there are 180 classes per day, then the number of teachers = 180/5 = 36

Answer: C

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Re: King School has an enrollment of 900 students. The school day consists  [#permalink]

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New post 13 Dec 2019, 19:58
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gmatt1476 wrote:
King School has an enrollment of 900 students. The school day consists of 6 class periods during which each class is taught by one teacher. There are 30 students per class. Each teacher teaches a class during 5 of the 6 class periods and has one class period free. No students have a free class period. How many teachers does the school have?

A. 25
B. 30
C. 36
D. 60
E. 150


PS15402.01



Since there are 900 students in the school and each student has to attend 6 classes, there are 900 x 6 = 5400 student-class units.

Since each teacher has to teach 5 classes and each class has 30 students, one teacher can manage 5 x 30 = 150 student-class units.

Therefore, we need 5400/150 = 36 teachers.

Answer: C
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King School has an enrollment of 900 students. The school day consists  [#permalink]

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New post 19 Dec 2019, 03:46
gmatt1476 wrote:
King School has an enrollment of 900 students. The school day consists of 6 class periods during which each class is taught by one teacher. There are 30 students per class. Each teacher teaches a class during 5 of the 6 class periods and has one class period free. No students have a free class period. How many teachers does the school have?

A. 25
B. 30
C. 36
D. 60
E. 150
PS15402.01



Totol no: of students = 900
No. of students/class = 30
No. of classes = 900/30 = 30
No. of periods/teacher = 5
No. of periods/day = 30*6 = 180

No. of teachers = 180/5 = 36
Option C
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King School has an enrollment of 900 students. The school day consists  [#permalink]

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New post 06 Jan 2020, 08:56
MBA HOUSE KEY CONCEPT: rule of 3 directly proportional

900 students

1 day = 6 class periods

1 class period = 1 teacher

30 students = 1 classroom

I00 students / 30 students = 30 classrooms x 6 class periods = 180 class periods / 5 teachers = 36 teachers.

C :dazed
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King School has an enrollment of 900 students. The school day consists  [#permalink]

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New post 18 Jul 2020, 06:53
gmatt1476 wrote:
King School has an enrollment of 900 students. The school day consists of 6 class periods during which each class is taught by one teacher. There are 30 students per class. Each teacher teaches a class during 5 of the 6 class periods and has one class period free. No students have a free class period. How many teachers does the school have?

A. 25
B. 30
C. 36
D. 60
E. 150

PS15402.01

Sharing my approach to this PS question

1. We are given that there are a total \(900\) students and there are \(30\) students per class. Hence, we have \(\frac{900}{30}\) \(=\) \(30\) classes
2. Each class has \(6\) periods, hence all \(30\) classes have \(30 * 6\) \(=\) \(180\) periods
3. Next, we are given that each teacher teaches \(5\) out of \(6\) periods, meaning that if there are \(n\) teachers then a total of \(5n\) periods are taught. And from step no. 2 we know that the value of \(5n\) is \(180\)
4. \(5n = 180\), hence \(n = 36\)

Ans. C
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King School has an enrollment of 900 students. The school day consists   [#permalink] 18 Jul 2020, 06:53

King School has an enrollment of 900 students. The school day consists

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